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We present a new approach to vortex methods for the 2D Euler equations. We obtain long-time high-order accuracy at almost optima I cost by using three tools: fast adaptive quadrature rules, a free-Lagrangian formulation, and a useful new analysis of the consistency error. Our error analysis halves the order of differentiability required of the flow and suggests an efficient new balance of smoothing parameters which works well with fast summation schemes. Numerical experiments with our methods confirm our theoretical predictions and display excellent long-time accuracy. (C) 1997 Academic Press.
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3.8
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1.6W
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